Expected utility as a measurement tool in the terrorism context

Classical criminology assumes that criminals are rational beings who weigh the costs and benefits of their actions. Gary Becker (1968) produced the first fully-fledged theory of crime based on rational behaviour. His research led to an upsurge of interest in the economics of criminal behaviour [see, for example, Isaac Ehrlich (1973), Ann Witte (1980), Ehrlich and George Brower (1987), James Andreoni (1991), Richard Freeman (1996), Steven Levitt (1997), Pablo Fajnzylber et al. (2000), inter alia.1

In his well-known work, Becker (1968) deals with the decision to engage in criminal activity or, as he calls it, a determination of the supply of offenses. He makes use of the orthodox model of decision-making under risk and uncertainty: expected utility theory. But when Becker (1968) says that the offender maximises expected utility and when he sketches an outline of the offender as a rational decision-maker, he uses expected utility theory more as a logical-formal construct than as a theory of measurement. Becker never actually measures utility.The same is true of Enders and Sandler’s (2002) application of Becker’s approach to the analysis of terrorist behaviour. The utility that the terrorist group expects to accrue from different actions is never measured. Expected utility theory is simply used as a way to structure the terrorist group’s decision-making process and predict some basic patterns. For example, that the expected utility of terrorism vis-a-vis legitimate activity can be impacted negatively by government security initiatives and, if the terrorist group seeks to maximise expected utility, such security initiatives may result in a re-ordering of its preferences in favour of legitimate activities. And so forth.

To go beyond the basic patterns that speak only of the choice between terrorism or crime and legitimate activity, expected utility theory could be used as it was intended. That is, to measure (see Fishburn 1989, p. 138). The principal idea and principal result presented by von Neumann & Morgenstern (1947) is that if a small number of seemingly self-evident rules or axioms2 are obeyed during the decisionmaking process, a utility function exists that allows for the preference ordering of some set of risky prospects (gambles or risky actions). Terrorist actions such as bombing, armed assault and hostage taking are risky prospects x,y,... with payoffs measured in some unit, say media attention, and occurring with some probability. For example, there might be a 5 percent chance that an assassination will generate more than 1,000 column inches of newspaper coverage. Economists would say that terrorist actions like bombing and armed assault and others form a set X and we use the symbol > to indicate that the terrorist prefers one action to another. A utility function и that orders the terrorist actions on X is:

For all terrorist actions in the set, one action x is preferred to another у if and only if (denoted by <=>) the utility function yields a higher value for x than for у .Von Neumann & Morgenstern (1947) set out to show that such a function or, rather, class of functions exists.The result, expected utility theory, is a contribution to representational measurement theory (see Boumans 2007), a branch of mathematics and logic that aims to establish a correspondence between some type of magnitudes (e.g. mass, velocity, dollars) and numbers (e.g. 1, 2,...). In expected utility theory, von Neumann & Morgenstern (1947) establish such a correspondence between payoffs (which might be monetary, fatalities, column inches or minutes of media attention etc.) and utility numbers where the magnitude of the former corresponds to the order or magnitude of the latter. If we ‘weight’ the utility numbers for each possible outcome by the probability that the outcome occurs and then add up all these weighted utilities, we get the expected utility for the action:

The perfectly rational terrorist group would choose the attack method with the highest expected utility. Even if we don’t believe that the terrorist group would choose optimally—by now it should be clear that such a belief has a reasonably high likelihood of being wrong on any given occasion—the expected utility theory provides the benchmark against which actual decisions can be compared. The preliminary step, computing u{xX is also important because it allows us to see how utility changes with changes in outcomes. One of the key reasons why expected utility theory exists is that the mathematical expectation or expected value of a gamble does a poor job of explaining human decision-making. People do not choose the option with the highest expected value. Rather, utility increases at a decreasing rate as outcomes increase and the decision-maker will usually prefer a sure payoff to a gamble with an expected value of the same amount. We can put these ideas into action by exploring the relationship between utility and payoffs to one of the most notorious terrorists of the twentieth century, Carlos the Jackal.

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